Upper-Bound Solutions to Tube Extrusion Problems Through Curved Dies

1972 ◽  
Vol 94 (4) ◽  
pp. 1108-1111 ◽  
Author(s):  
K. T. Chang ◽  
J. C. Choi
Keyword(s):  
Upper Bound ◽  
Cone Angle ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Die Geometry ◽  
Tube Extrusion

Velocity fields of tube extrusion problems through curved dies are presented for an incompressible material. These velocity fields are also applicable to conical and square-cornered dies. Thus, in principle, upper bound solutions for tube extrusion problems through arbitrarily shaped dies are obtained. As an illustration, tube extrusion processes through conical dies of small cone angle have been treated. Effect of die geometry and friction is presented graphically.

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

Plane Strain Forging—A Lower Upper Bound Approach

1975 ◽  
Vol 97 (1) ◽  
pp. 119-124 ◽  
Author(s):  
V. Nagpal ◽  
W. R. Clough
Keyword(s):  
Velocity Field ◽  
Process Parameters ◽  
Upper Bound ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Special Cases ◽  
Rectangular Strip ◽  
General Velocity

A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.

Calculation of Punch Force and Maximum Pressure for Tube Extrusion

2000 ◽  
Author(s):  
S.-H. Zhang ◽  
Y.-L. Shang
Keyword(s):  
Upper Bound ◽  
Physical Modeling ◽  
Steel Tube ◽  
Experimental Results ◽  
Maximum Pressure ◽  
Punch Force ◽  
Tube Extrusion ◽  
Tooling System ◽  
Very High ◽  
Good Agreement

Abstract Punch force and maximum pressure for tube extrusion can be predicted with an upper bound theory-based program POLSK. Experiments of steel tube extrusion and wax physical modeling were performed. The punch force and the maximum pressure values were obtained. Comparisons were made among the experimental results, physical modeling results and upper bound predictions. It was found that a medium extrusion coefficient causes the lowest pressure on the tooling system, very low and very high extrusion coefficients can both cause very high pressure. It is proved that the upper bound predictions are in good agreement with the experimental results and the upper bound program is suitable for use of steel tube extrusion design.

Upper bound limit analysis of masonry retaining walls using PIV velocity fields

Meccanica ◽  
2017 ◽  
Vol 53 (7) ◽  
pp. 1661-1672 ◽  
Author(s):  
Benjamin Terrade ◽  
Anne-Sophie Colas ◽  
Denis Garnier
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Retaining Walls ◽  
Velocity Fields ◽  
Upper Bound Limit Analysis

Analysis of Strip Rolling by the Upper Bound Approach

1987 ◽  
Vol 109 (4) ◽  
pp. 338-346 ◽  
Author(s):  
B. Avitzur ◽  
W. Gordon ◽  
S. Talbert
Keyword(s):  
Velocity Field ◽  
Rigid Body ◽  
Upper Bound ◽  
Velocity Fields ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Total Power ◽  
Strip Rolling ◽  
Upper Bound Technique ◽  
Independent Process

The process of strip rolling is analyzed using the upper bound technique. Two triangular velocity fields, one with triangles in linear rigid body motion and the other with triangles in rotational rigid body motion, are developed. The total power is determined as a function of the four independent process parameters (relative thickness, reduction, friction and net front-back tension). The results of these two velocity fields are compared with the established solution from Avitzur’s velocity field of continuous deformation. Upon establishing the validity of the triangular velocity field as an approach to the strip rolling problem, recommendations are suggested on how this approach can be used to study the split end or alligatoring defect.

A New Upper-Bound Method for Analysis of Some Steady-State Plastic Deformation Processes

1969 ◽  
Vol 91 (3) ◽  
pp. 731-741 ◽  
Author(s):  
E. R. Lambert ◽  
H. S. Mehta ◽  
S. Kobayashi
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Plane Strain ◽  
Velocity Component ◽  
Velocity Fields ◽  
Flow Lines ◽  
Upper Bound Method ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Deformation Processes

A method of obtaining admissible velocity fields without velocity discontinuities is described, and applied to plane-strain extrusion, tube extrusion, and axisymmetric piercing. In plane-strain extrusion, the flow lines, grid distortions, and extrusion pressures were obtained and the values were compared with those found in previous solutions. For tube extrusion and axisymmetric piercing, the solutions are presented as examples in terms of flow lines and velocity component distributions; these solutions await experimental confirmation.

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